Pythagorean Fuzzy Set for Enhancement of Low Contrast Mammogram Images

Abstract

Breast masses are often one of the primary signs of breast cancer, and precise segmentation of these masses is essential for accurate diagnosis and treatment planning. Diagnosis may be complex depending on the size and visibility of the mass. When the mass is not visible clearly, precise segmentation becomes very difficult and in that case enhancement is essential. Inadequate compression, patient movement, or paddle/breast movement during the exposure process might cause hazy mammogram images. Without enhancement, accurate segmentation and detection cannot be done. As there exists uncertainties in different regions, reducing uncertainty is still a main problem and so fuzzy methods may deal these uncertainties in a better way. Though there are many fuzzy and advanced fuzzy methods, we consider Pythagorean fuzzy set as one of the fuzzy sets that may be powerful to deal with uncertainty. This research proposes a new Pythagorean fuzzy methodology for mammography image enhancement. The image is first transformed into a fuzzy image, and the nonmembership function is then calculated using a newly created Pythagorean fuzzy generator. Membership function of Pythagorean fuzzy image is computed from nonmembership function. The plot between the membership value and the hesitation degree is used to calculate a constant term in the membership function. Next, an enhanced image is obtained by applying fuzzy intensification operator to the Pythagorean fuzzy image. The proposed method is compared qualitatively and quantitatively with those of non-fuzzy, intuitionistic fuzzy, Type 2 fuzzy, and Pythagorean fuzzy methods, it is found that the suggested method outperforms the other methods. To show the usefulness of the proposed enhanced method, segmentation is carried out on the enhanced images.